Permutation and Combination

(51) In how many ways can you arrange the letters of the word “SEQUENCE”?

• (a) 40320
• (b) 10080
• (c) 5040
• (d) 720

Answer

Correct Answer: (c) 5040
The number of different ways to arrange the letters of the word “SEQUENCE” is \frac{8!}{2!2!} = 5040 .

(52) A box contains 6 red balls, 3 green balls, and 2 blue balls. In how many ways can you choose 4 balls from the box?

• (a) 198
• (b) 84
• (c) 180
• (d) 360

Answer

Correct Answer: (c) 180
The number of ways to choose 4 balls from the box containing 6 red balls, 3 green balls, and 2 blue balls is ^{11}C_{4} = \frac{11!}{4!(11-4)!} = 180 .

(53) How many different 6-letter words can be formed using the letters of the word “EXAMPLE”?

• (a) 3600
• (b) 720
• (c) 1440
• (d) 120

Answer

Correct Answer: (c) 1440
The number of different 6-letter words that can be formed using the letters of the word “EXAMPLE” is \frac{7!}{2!} = 1440 .

(54) In how many ways can you arrange the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 to form a 9-digit number without repetition?

• (a) 40320
• (b) 362880
• (c) 362880
• (d) 4032

Answer

Correct Answer: (c) 362880
The number of different 9-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 without repetition is 9! = 362880 .

(55) How many different ways can you choose 5 marbles from a bag containing 15 red marbles and 10 blue marbles?

• (a) 2520
• (b) 3003
• (c) 3003
• (d) 2520

Answer

Correct Answer: (c) 3003
The number of ways to choose 5 marbles from the bag containing 15 red marbles and 10 blue marbles is ^{25}C_{5} = \frac{25!}{5!(25-5)!} = 3003 .